I highly recommend Mickey's Dairy Bar on the east side of Madison, WI for breakfast. For dinner, see if Dotty's Dumpling's Dowry is still around for fantastic burgers, or cruise State Street (which you should wander up and down anyway, just because it's so lovely). I also highly recommend Himal Chuli, a very inexpensive Nepalese restaurant (vegetarian) for lunch or dinner.

I wrote in the Hamburger forum about Sioux Sundries, in Harrison Nebraska, on the Wyoming border, also not far from Mt Rushmore/Black Hills. If you go nowhere else on your trip, you must go here. It is the essence of homey, the biggest, and best tasting cheeseburger I've ever had. The town is the only town in a county, twice the size of Rhode Island, with only 1,400 residents. Here is a link to this overlooked masterpiece: http://net.unl.edu/nextexit/winding/pounds_01.html